Assume that P(E) = 0.471 and P(F) = 0.595. If E and F are independent, find P(E and F)

Answer:

D) (0,9.5) and (10,1.5)

Step-by-step explanation:

a line of best fit is a line that is drawn through the data points on the scatter plot. Option D is the only answer that draws a linear line through the data points.

Option A makes a short line above the points. if the line is not through the points, it doesn't work

Option B is drawing a positive line (as in it's increasing) and therefore cannot work

Option C draws a line below the points and does not represent the line of best fit for this scatter plot

Answer:

3  1/2  pints

Step-by-step explanation:

A pint is two cups

7 cups  /  2cups/pint =   7/2 pint = 3  1/2 pints

Answer:

544 words

Step-by-step explanation:

The number of 4 letter words can be constructed from ABCDE would be 5^4 = 625

The number of  4 letter words can be constructed using BCD would be 3^4 = 81

So the number of words that use at least one vowel would be  5^4 - 3^4  =  625-81 = 544

Durante la celebración familiar del cumpleaños y aplicando las propiedades de los números fraccionarios, el hijo menor recibió 5/14 de la torta.

En esta pregunta tenemos una torta de cumpleaños, que asumimos de forma circular. Si leemos con cuidado el enunciado, encontramos que la proporción del pastel correspondiente al cumplimentado mediante la siguiente sustracción de fracciones:

x = 1 - 1/7 - 3/14 - 2/7

x = 6/7 - 3/14 - 2/7

x = 4/7 - 3/14

x = 8/14 - 3/14

x = 5/14

Durante la celebración familiar del cumpleaños y aplicando las propiedades de los números fraccionarios, el hijo menor recibió 5/14 de la torta.

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medians of a triangle is triangle 4

[tex]f(3) = 1 \: \: \: \: \: \: \: \: f(7) = 3[/tex]

[tex] \frac{f(7) - f(3)}{7 - 3} = \frac{3 - 1}{4} = \frac{2}{4} = 0.5[/tex]

Answer:

Discrete mathematics is the study of mathematical structures that can be considered "discrete" rather than "continuous". Objects studied in discrete mathematics include integers, graphs, and statements in logic.

Hence, the correct answer is (c)$1,055.10

Simple interest is interest calculated on the principal portion of a loan or the original contribution to a savings account. Simple interest does not compound, meaning that an account holder will only gain interest on the principal, and a borrower will never have to pay interest on interest already accrued.

We have,

Amount spent each month = $83.42

Interest rate, r = 1.8% = 0.018

Time, n = 3 years

Now,

The total amount collected at the end of the year = $83.42 × 12 = $1001.04

The value of the amount deposited in the bank after 3 years will be

Future value = Present value × ( 1 + r )ⁿ

on substituting the respective values,

we have

Future value = $1001.04 × ( 1 + 0.018 )³

or

Future value = $1,056.07

Hence,

The money he could have at the end of 3 more years will be $1,055.17

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Answer:

2²X3³=36

Step-by-step explanation:

hope this helps you (✿❛◡❛)

Answer:

59 degrees

Step-by-step explanation:

Supplemental means that the angles add to 180.

x + y + z = 180

x + y = 2z + 3

Replace x + y  in the top equation with 2z + 3

2z + 3 = z = 180

3x + 3 = 180 Combine the z's.

3x = 177 subtract 3 from both sides

x = 59

Using the combinations formula, the probability that you'll win the jackpot is given by:

A. 1/302575350.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

5 numbers are selected from a set of 70, along with one number from a set of 25, hence the number of combinations is given by:

[tex]C_{70,5}C_{25,1} = \frac{70!}{5!65!} \times \frac{25!}{1!24!} = 302575350[/tex]

Only one combination is correct, hence the probability of winning is given by:

A. 1/302575350.

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Answer:

16 pieces

Step-by-step explanation:

(100*100)-(25*25)=16

Answer:

Length equals to 75 ft

Step-by-step explanation:

A=l x w           Area of a rectangle formula.

A/w=l              Solve for length

300=l x 4      

300=l x 4

4           4

300/4=l

75=l

Answer:

Step-by-step explanation:

[tex]\frac{19}{x}[/tex] = tan 29°

x = [tex]\frac{19}{tan29^o}[/tex] ≈ 34.28

242 inches

Step-by-step explanation:

with an 11 inch diameter, a single spiral of the wires circumference is about 22 inches. with this we can multiply 22 by 11 and assume its 242 inches long

The equation of the circle is (x + 7)² + (y + 6)² = 4 if the center and radius are (-7,-6) and 2 respectively.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have center of the circle(h, k) = (-7, -6)

The radius of the circle r = 2

The standard form of a circle:

(x - h)² + (y - k)² = r²

(x - (-7))² + (y - (-6))² = 2²

(x + 7)² + (y + 6)² = 4

Thus, the equation of the circle is (x + 7)² + (y + 6)² = 4 if the center and radius are (-7,-6) and 2 respectively.

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Using continuous compounding, it is found that:

a) The account will be worth $26,916.31 in 10 years.

b) It will take 42.18 years for the account to be worth $70,000.

The amount of money earned, in continuous compounding, after t years, is given by:

[tex]A(t) = Pe^{rt}[/tex]

In which:

The parameters are given as follows:

A(0) = 20000, r = 0.0297, t = 10.

Hence the worth in 10 years will be given by:

[tex]A(t) = Pe^{rt}[/tex]

[tex]A(10) = 20000e^{0.0297 \times 10}[/tex]

A(10) = $26,916.31.

Now, we find in how many years it will be worth $70,000, as follows:

[tex]A(t) = Pe^{rt}[/tex]

[tex]70000 = 20000e^{0.0297t}[/tex]

[tex]e^{0.0297t} = 3.5[/tex]

[tex]\ln{e^{0.0297t}} = \ln{3.5}[/tex]

[tex]0.0297t = \ln{3.5}[/tex]

[tex]t = \frac{\ln{3.5}}{0.0297}[/tex]

t = 42.18 years.

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The system of equations represented by the graph is the one in option b.

We can see that the graph is:

A solid line with a positive slope, such that the region above the line is shaded.

This is represented by:

y ≥ line.

And we can see a horizontal line at y = 4, the line is dashed and the region below the line is shaded, then we have:

y < 4

Then the system is of the form:

y ≥ line.

y < 4

The only option that has that form is option B, so that is the correct one.

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Answer: 5 rides (for a cost of $35)

Step-by-step explanation:

   The solution to your problem is the point of intersection. This is where the lines intersect, or cross over, each other. We can extend the lines to find the answer. See attached.

   They intersect at point (5, 35) which represents 5 rides and 35 dollars.

Answer:

6/2^2=36/4

so it will be 36/4+14/1

taking LCM As 4 it will come out

36+56/4 =92/4=23

Step-by-step explanation:

hope this helps ʕ´•ᴥ•`ʔ

Answer:

23

Step-by-step explanation:

(6/2) ^2 +7*2

We need to solve this using the order of operations

First, solve the item in parentheses

6/2 =3

(3) ^2 +7*2

Then calculate the exponential term

3^2 = 9

9 + 7*2

Then multiply

7*2 = 14

9+14

Finally add

23

The size of a triangle side is proportional to its opposite angle. The largest side is opposite to the largest angle while the smallest side is opposite to the smallest angle.

An equation is an expression that shows the relationship between two or more numbers and variables.

The size of a triangle side is proportional to its opposite angle. The largest side is opposite to the largest angle while the smallest side is opposite to the smallest angle.

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Answer:

2,4,9,16

Step-by-step explanation:

2

4

9

16

are range because they are exactly opposite of domain

Based on the calculations, the amount of money she invested is equal to $3,520.

First of all, we would assign variables to the amount of money that he invested at different interest rates as follows:

Since Lydia invested the same amount of money in both stocks, we have:

x = y     ....equation 1.

At the two interest rates, the total amount Lydia gets is given by:

0.11x + 0.14y = 440     ....equation 2.

Solving the equations simultaneously, we have:

0.11y + 0.14y = 440

0.25y = 440

y = 440/0.25

y = $1,760.

Thus, the total investment is given by:

Total investment = 1760 + 1760

Total investment = $3,520.

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Answer:

24

Step-by-step explanation:

7x4

Using the expected value of a discrete distribution, the values are given as follows:

a) $250.

b) $2,500,000.

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

The distribution of the company's earnings is given as follows:

Considering that the policy sells for $600, for example, a $5000 claim is a loss of $5000 - $600 = $4,400 for the company, which explains the above distribution.

Item a:

The expected value for a policy sold is given by:

E(X) = 600(0.965) - 4400(0.02) -9400(0.01) - 29400(0.005) = 250.

Item b:

Considering the value found in item a for a single policy, for 10,000 policies, the expected profit is given by:

E = 10000 x 250 = 2,500,000.

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The true statement is the value of f(2) is larger than the value of f(3).

The function is given as:

f(x) = −3x^2 + 4x + 6

Calculate f(2) and f(3), as follows:

f(2) = −3(2)^2 + 4(2) + 6 = 2

f(3) = −3(3)^2 + 4(3) + 6 = -9

By comparison;

f(2) is greater than f(3) because 2 > 9

Hence, the true statement is the value of f(2) is larger than the value of f(3).

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The graph of f(x) has been reflected across the y-axis and stretched by a factor of 2 ,  Option E is the correct answer.

A function is a law that relates a dependent and an independent variable.

It is given that f(x) = x³

g(x) = -2x³

When a function is reflected along an axis , the coordinate of that axis remains the same but the coordinate of the other axis becomes negative

So, if x coordinate is transformed to -ve of the parent function , The function is reflected along y axis.

As there is 2 in front of the parent function ,

f'(x) = a f(x) , represents vertical stretch when a >1

Therefore The graph of f(x) has been reflected across the y-axis and stretched by a factor of 2 , Option E is the correct answer.

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Usando un sistema de ecuaciones, se encuentra que la expresión que muestra la cantidad total que gastará en pizarras y marcadores es:

G = 0.75b + 0.5m.

¿Qué es un sistema de ecuaciones?

Un sistema de ecuaciones es cuando dos o más variables están relacionadas y las ecuaciones se construyen para encontrar los valores de cada variable.

En este problema, las variables son:

Considerando el precio de cada producto(cada tablero = $0.75, cada marcador = $0.5), la expresión que muestra la cantidad total que gastará en pizarras y marcadores es:

G = 0.75b + 0.5m.

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[tex]\large\displaystyle\text{$\begin{gathered}\sf 7+5y=-13 \end{gathered}$}[/tex]

Subtract 7 from both sides.

[tex]\large\displaystyle\text{$\begin{gathered}\sf 5y=-13-7 \end{gathered}$}[/tex]

Subtract 7 from −13 to get −20.

[tex]\large\displaystyle\text{$\begin{gathered}\sf 5y=-20 \end{gathered}$}[/tex]

Divide both sides by 5.

[tex]\large\displaystyle\text{$\begin{gathered}\sf y=\frac{-20}{5} \end{gathered}$}[/tex]

Divide −20 by 5 to get −4.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf y=-4 \end{gathered}$} }\large\displaystyle\text{$\begin{gathered}\sf \ \ \to \ \ \ Answer \end{gathered}$}[/tex]

We let y = -4.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{7+5\times-4=-13 \ \ \to \ \ [ Multiply] } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{7-20 \ \ \to \ \ [Subtract] } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{-13=-13 \ \ \to \ \ [ Equality \ holds ]} \end{gathered}$}[/tex]

Answer:

5y= -13-7

5y=-20

5y = -20

5 = 5

y = -4